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Anh T. Le and Timothy C. Steimle*
The molecular frame electric dipole
moment and hyperfine interaction in
hafnium fluoride, HfF. Department of Chemistry and Biochemistry, Arizona State
University,Tempe, AZ 85287
Petersburg Nuclear PhysicsInstitute, Gatchina, 188300, Russia
and Quantum Mechanics Division, St. Petersburg State University, St.
Petersburg 198904, Russia.
Leonid Skipnikov and Anatoly V. Titov
*Funded by NSF
The 68th International Symposium on Molecular Spectroscopy, June 2013
J. Chem. Phys. 138, 124313 (2013)
Electron’s Electric dipole moment measurement
PbO, YbF, PbF, ThO, WC, HfF+, HfH+, PtH+, PtF+, ThH+, ThF+...
small W-doubling easily polarized small Zeeman tuning.
Minimizes systematic errors
The 3D1 state:
Focus on HfF (not HfF+ ): Provide the hyperfine parameters, molecular dipole moments of
HfF
el HfF(theory) Calculated hyp. parameters, molecular dipole moments
Experimental values (hyp. Parameters, molecular dipole moments)
Comparisonel HfF+
Improve
PNC needed information (Wa, Ws, Wd)
Calculate
Previous Related Work on HfF – not much
Adam et al.(2004): J. Mol. Spectroc. 2004, 225, 1
Fine structure parameters for 9 bands in the range 17000-24000cm-1
Moskvitina et al.(1999):Spectrosc. Letts., 1999, 32(5), 719
Identify 3 bands: 589nm, 590.6 nm, 593.1 nm – Not analyzable
Motivated by eEDM experiments
Grau et al. (2012): J. Mol. Spectroc., 2012, 272, 32
8 bands recorded, rotationally assigned, analyzed 13400-14500cm-1
Barker et al. (2011):J. Chem. Phys. 2011, 134, 201102
REMPI study HfF, ZEKE study HfF+
Loh et al. (2012):J. Mol. Spectroc. 2012, 276-277, 49
REMPI study, transition in the excited state up to 33000cm-1
Experiment method
Ablation laser
CW dye laser
Skimmer
Stark Plates
Well collimatedmolecular beamRot.Temp.<20 K
Electric field > 4000 V/cmResolution ~30 MHz
Gated photon counter
%Abundance
I gN Q (mBarns
)177Hf 18.60 7/2 0.2571 +3365179Hf 13.62 9/2 -0.1574 +3793
180Hf 35.08 0 _ _
19F 100 1/2 5.376 _
Overview
177HfF R(11/2) 179HfF R(15/2)
NOTE: highly overlapped with 180HfF, Complicated spectra (WHY? Next slide)
Q (2H)=2.860(mBarns)
180HfF180HfF
Why are the spectra complicated ? (Cont.)177HfF R(11/2) (I=7/2)
J=5.5
X2D3/2
J=6.5
(v=1)[17.9]2.5
Rotation Mag. hyperfine(177Hf) [Mag.+Qua.] (177Hf)
9
8
7
6
5
4
3
2
10
9
8
7
6
5
4
3
F
9
8
65,7
4
3
2
10
83
9
7,6,5,4
F
J+I(7/2)=F
1. Effective Hamiltonian
Heff = Hso+ Hrot + Hmhf(Hf)+ HeQq(Hf)
Modeling the (1,0)[17.9]2.5-X2D3/2 band system
2. Matrix representation: Hund’s case (abJ) coupled basis set:
Eigenvalues & Eigenvectors
Parameters: B, h3/2(177,179Hf) and eQq0(177,179Hf) for the
X2D3/2(v=0) state,T00, B, h5/2(177,179Hf) and eQq0(177&179Hf) for the
[17.9]2.5(v=1) state
Observation & prediction 177HfF R(11/2)
Laser wavenumber (cm-1)
LIF
Sig
nal
Total Angular momentum, F
Rela
tive
Ener
gy L
evel
(cm
-1)
X2D3/2, J=5.5
(v=1)[17.9]2.5, J=6.5
ABCDEF
abcd
abcd
ABCDEF
ΔF=+1ΔF= 0
Observed
Pred.
180HfF
Observation & prediction of 179HfF R(15/2)(v=1)[17.9]2.5,
J=17/2
Rela
tive
Ener
gy L
evel
(cm
-1)
X2D3/2, J=15/2
LIF
Sig
nal
Laser wavenumber (cm-1)
A
B,C
G
DE
F H I K
ABCDEFGHIK
ΔF= +1
Observed
Pred.
180HfF
Stark Shift (MHz)
LIF
Sig
nal
(v=1)[17.9]2.5, J=5/2
X2D3/2, J=3/2
Electric Field Strength (V/cm)
En
erg
y S
hift
(MH
z)
1732.0 V/cm ||
1732.0 V/cm
Field FreeR(3/2)
Observation-Stark Shifts 180HfF
A B C D
a c e gb d f h
DCBA geca h fdb
ΔMF= 0ΔMF= -1
ΔMF= +1
Determined parameters
*CCSD(T) calculation - collaboration with Prof. Titov
gI(177Hf)
gI(179Hf)-1.59
hW(177Hf)
h W (179Hf)-1.68(16)
StatesX2D3/2
hW(179Hf)
[17.9]2.5 (v=1)
-0.00348(34) -0.01660(26)
0.02572(27)0.00586(38)hW(177Hf)
Predicted ratio
-1.55(3)
Q(177Hf)
Q(179Hf)0.89eQq0(177Hf)
eQq0(179Hf)
eQq0(177Hf)
eQq0(179Hf)
-0.0805(35) -0.2101 (43)
-0.1998(36)-0.0774(30)
0.96(8) 0.95(6)
0.0056(8)*
-0.0930(66) *
Para-meters
Discussion-Are the parameters realistic?1.Field Free Spectra
MO correlation diagram
h3/2(177HfF(experiment)): 176(11)MHz
Unpaired e is Hf-centered (5d2)
Predicted molecular magnetic
hyperfine parameter
h3/2(177Hf)=170 MHz
Atomic hyperfine of Hf
3F[Xe].4f14.5d2.6s2
…2s21d13s2 2D3/2
m(X2D3/2)=1.66(1) D
m([17.9]2.5(v=1))=0.419(7) D
Electron configuration of HfF
6s2(Hf)
mind mbond
mtot
Small m
F-Hf+
Why does HfF have small dipole moment?
2. Stark Spectra
Discussion-Are the parameters realistic?
(cont.)Determined molecular dipole moments:
Elec. Neg.Hf: 1.3F: 3.98
Large Dipole moment
Experiment:
Calculation CCSD(T): m(X2D3/2)= 1.63 D(collaboration with Prof. Titov)
Summary
• The molecular electric dipole moments of the
[17.9]2.5(v=1) and X2D3/2 (v=0) states from optical
Stark spectrum
• The complicated spectra of (1,0)[17.9]2.5-X2D3/2 have
been recorded and completely analyzed to provide
magnetic hyperfine and quadrupole parameters
• ab initio calculations using scalar-relativistic, coupled
cluster, method with single and double cluster
amplitudes (CCSD) of the 2Δ3/2 state properties were
performed by Prof. Titov. Calculated values are in
good agreement with the experimental values.
Thank you
NSF Funding sources:
Prof. Anatoly V. Titov (Petersburg Nuclear Physics
Institute)
Collaborations:
Group members: Dr. Fang Wang
Ruohan Zhang
Advisor: Prof. Timothy C. Steimle